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 Tr. Mat. Inst. Steklova, 2018, Volume 300, Pages 86–94 (Mi tm3856)

Evolution of a condensation surface in a porous medium near the instability threshold

A. T. Il'icheva, G. G. Tsypkinb

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526 Russia

Abstract: We consider the dynamics of a narrow band of weakly unstable and weakly nonlinear perturbations of a plane phase transition surface separating regions of soil saturated with water and with humid air; during transition to instability, the existing stable position of the phase transition surface is assumed to be sufficiently close to another phase transition surface that arises as a result of a turning point bifurcation. We show that such perturbations are described by a Kolmogorov–Petrovskii–Piskunov type equation.

 Funding Agency Grant Number Russian Science Foundation 16-11-10195 This work is supported by the Russian Science Foundation under grant 16-11-10195.

DOI: https://doi.org/10.1134/S0371968518010065

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 300, 78–85

Bibliographic databases:

UDC: 532.546

Citation: A. T. Il'ichev, G. G. Tsypkin, “Evolution of a condensation surface in a porous medium near the instability threshold”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Tr. Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 86–94; Proc. Steklov Inst. Math., 300 (2018), 78–85

Citation in format AMSBIB
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